Changing Phases: Detecting Other Worlds With The Fade In/Fade Out

Nov. 01, 2001

by Laurance Doyle - Astronomer

One night at the observatory I was preparing to view an eclipsing binary star that was going to be close to the full moon. I was worried that it might be too close, which would ruin the brightness measurements I needed to determine exactly when the two stars orbited in front of each other (see "The do-si-do" method of detecting extrasolar planets). Suddenly it hit me! Why, planets around other stars must also go through this change of phase from full to new, just like the

Quickly I did a calculation. I knew that seen from far away in visible light that Jupiter (by reflected light) would appear to be about one-billionth the brightness of the Sun. This is why planets cannot easily be seen orbiting their starsthe contrast in brightness washes out the planets. But some of the newly discovered inner giants ("hot Jupiters" as they are called) were known to be 100 times closer to their stars.

If you hold a ruler up and note its angular size, and then move it twice as far away, you will notice it now subtends 1/2 the angle it did before. If you hold it horizontally, youll get the same effect only the ruler is now 1/2 the angular width. A piece of paper (or a star's disc, for that matter) will halve in both the vertical and horizontal directions when it is placed twice as far away, so that the paper will appear to have 1/4th the area it had at half the distance. This is the inverse square lawthe apparent area of something is 1/4 the previous area at twice the distance, 1/9th the area at three times the distance, 1/16th the area at four times the distance, and so on.

By putting a "Jupiter" 100 times closer, it will reflect 10,000 times the light. Doing this with Jupiter would make it appear to be not one-billionth, but one hundred-thousandth the brightness of the Sun. That may not seem like much more, but it would now become detectable at the very limits of precise photometry.

To measure the brightness change in a star due to a planet going through its phases around it requires measuring a fractional brightness change of about one part in 100,000. This is not currently possible from Earth using any known optical telescope. However, it is possible from space for a specially built telescope. And the Kepler Spacecraft Mission will use just such a telescope to measure the tiny drop in the brightness of a star due to the transit of Earth-sized planets moving across the star's disc (see the "Wink Method").

One of the most interesting things about this method is that it does not require the planet to move across the disc of the star; for most all inclinations of this hot-Jupiter's orbit, it will show a change of phase, causing a sinusoidal variation in the brightness of the star every orbit. According to the calculations of the Kepler Mission team, this new method should allow the discovery of about 1700 additional hot-Jupiters during the lifetime of the mission, more than doubling the number of planets initially predicted.

If these variations can be very well measured, the phase function of the planets can also be obtained. The phase function is how much light is reflected off the planet's surface with illumination angle. With our Moon the phase function is quite "steep." This means that the Moon gets much brighter during its full phase than with its quarter phase (the full Moon is 9 times brighter than the quarter Moon). This is because its surface is rough. When illumined by the Sun during quarter phase, the rough surface "bounces" light all around, (this is called "multiple scattering"). But when illuminated straight on, as with the full Moon, virtually all the light that is not absorbed by the lunar soil is reflected back to us. (Even so, the Moon is about as reflective as a piece of coal.)

Thus, if we can discover hot-Jupiters in this way, we might also be able to tell what their surface roughness is like, as well. Of course, the point of the Kepler Mission is to find "Earths." But if the theory that hot-Jupiters form outside their solar systems and migrate inward were true, then they would tend to wipe out any Earth-like planets that had been in the way.

Of course, if "Earths" are found by the Kepler Mission in the same systems as hot-Jupiters, it will have to be "back to the drawing board" for this theory. Observations of extrasolar planets have yielded one surprise after another. I'd be amazed if there weren't a whole lot more surprises to come!

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Changing Phases: Detecting Other Worlds With The Fade In/Fade Out